I found that the hook that locks the folding stem to the rear fender was really loose so I dug out the T-handled wrench it came with and tightened it up. Nothing else appeared loose but I found what looked like two set screws beneath the folding mechanism and got a little turn out of each. I think they hold the rubber bushing in place where the stem rests against the base mechanism when unfolded so I probably damaged the rubber bushings by tightening them... but it did restore the “click!” sound I am supposed to get when unfolding.
Setting the charge level back to 100% does stop it from turning itself on and off when it is fully charged, but the app recommends setting it to 80% for daily use. We are using it many times a day so we set it back to 80% and just have to deal with the power-cycling issue that causes.
I never heard back from Segway support, which is a shame since their support was the reason I paid twice as much as the GoTrax. Might have to take it back to Costco. Also, the front tire is wearing out extremely fast. The center tread was nearly gone in barely a week and under 50 miles and is long gone now with wear continuing through the remaining tread.